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Square Numbers and Square Roots


Bruce is nearing the very end of Life of Fred Fractions, and one of the last lessons was about square numbers and square roots.  He had learned these concepts a while ago, when I taught him the basics of multiplying, but he was unfamiliar with the square root sign.  This lesson was a good review.  To me, it is also a perfect example of how a Constructivist approach to teaching mathematics solidifies conceptual understanding.

First we built out multiples of 2, 3, and 4.  Then we looked to see which arrays were square, and which were rectangle.

Next we labeled all of the numbers.  I then asked Bruce to identify the “square” numbers.

Since we hadn’t built out the fives, I had Bruce square 5 on the whiteboard.

We then moved onto the concept of square roots.  Bruce is still a bit confused on this point.  To be fair, we had just started the square root portion of the lesson when Jenna came running in and scattered all of the blocks!  We’ll have to try again later.


  1. JuneBug says:


    I’m 27 and consider myself pretty good at maths but I just fully understood squares and square roots after reading this post! I knew 2 squared is 4 and 9 squared is 81 but I never thought of it in terms of making a square with that length. It makes so much sense! Just by figuring that out, I realize the square of double any number is 4 times that number squared e.g. 220 squared is 110 squared times 4!

    Thanks for the revelation! I crammed a lot growing up and have learned so much from your blog! Looking fwd to teaching my kids

    • jenbrdsly says:

      I was blown away when I first saw square numbers made with number tiles too. I had always learned math by just memorizing formulas, but actually “doing” and “seeing” math is so much stronger. Thanks for being a blog reader! 🙂

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